Influence of surface geometry on metal properties

ABSTRACT

The influence of surface geometry on metal properties is studied within the limit of the quantum theory of free electrons. It is shown that a metal surface can be modified with patterned indents to increase the Fermi energy level inside the metal, leading to decrease in electron work function. This effect would exist in any quantum system comprising fermions inside a potential energy box. Also disclosed is a method for making nanostructured surfaces having perpendicular features with sharp edges.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Divisional application of U.S. patent applicationSer. No. 10/508,914, filed Sep. 22, 2004, and now U.S. Pat. No.7,074,498, which is the U.S. national stage application of InternationalApplication PCT/US03/08907, filed Mar. 24, 2003, which internationalapplication was published on Oct. 9, 2003, as International PublicationWO03083177 in the English language. The International Application claimsthe benefit of U.S. Provisional Application Ser. No. 60/366,563, filedMar. 22, 2002, U.S. Provisional Application Ser. No. 60/366,564, filedMar. 22, 2002, and U.S. Provisional Application Ser. No. 60/373,508,filed Apr. 17, 2002. The International Application is related toco-pending U.S. patent application Ser. No. 10/234,498, filed 3 Sep.2002, which claims the benefit of U.S. Provisional Application Ser. No.60/316,918, filed 2 Sep. 2001. The above-mentioned patent applicationsare assigned to the assignee of the present application and are hereinincorporated in their entirety by reference.

TECHNICAL FIELD

The present invention is concerned with methods for increasing the Fermilevel of a metal and for promoting the transfer of elementary particlesacross a potential energy barrier. The present invention also relates tomaking a surface having a geometric pattern for nanoelectronicsapplications, and more particularly, to making a surface having ageometric pattern that creates a wave interference pattern thatfacilitates the emission of electrons from the surface.

BACKGROUND ART

Surfaces having geometric patterns are used in a variety ofapplications. Generally, a laser, chemical, or other means etchesgeometric patterns on a surface of solid materials, such as silicon,metal, and the like, for example, as described in U.S. Pat. No.5,888,846. Geometric patterns may be used for creating optical diskstorage systems, semi-conductor chips, and photo mask manufacturing, asdescribed in U.S. Pat. No. 5,503,963. Surfaces capable of enhancing thepassage of electrons through a potential energy barrier on the borderbetween a solid body and a vacuum, such as those described in U.S. Pat.Nos. 6,281,514 and 6,117,344, should have patterns of the dimensions of5-10 nm.

Recent development of such technologies as electron beam milling and ionbeam lithography enable the fabrication of structures with dimension assmall as a few nanometers. Those low dimensions are comparable with thede Broglie wavelength of a free electron inside the metal. Because ofthis, it has become possible to fabricate some microelectronic devicesworking from the wave properties of the electrons [N. Tsukada, A. D.Wieck, and K. Ploog “Proposal of Novel Electron Wave Coupled Devices”Appl. Phys. Lett. 56 (25), p.2527, (1990); D. V. Averin and K. K.Likharev, in Mesoscopic in Solids, edited by B. L. Al'tshuler, P. A.Webb (Elsevier, Amsterdam, 1991)].

The general case of an elementary particle in the potential energy boxis depicted in FIG. 1. The behavior of a particle in the ordinarypotential energy box (OPEB) is well known. The Schroedinger equation forparticle wave function inside the OPEB has form [L. D. Landau and E. M.Lifshits “Quantum Mechanics” (Russian), Moscow 1963.]:d2ψ/dx2+(8π2m/h2)Eψ=0   (1)

Here ψ is the wave function of the particle, m is the mass of theparticle, h is Planck's constant, and E is the energy of the particle.Equation (1) is written for the one dimensional case. General solutionof (1) is given in the form of two plane waves moving in directions Xand −X:ψ(x)=Aexp(ikx)+Bexp(−ikx)  (2)

here A and B are constants and k is the wave vector:k=[(2mE)^(1/2)]/ (h/2π)  (3)

It is well known that in the case of U=∞, the solution for equation (1)is defined by the boundary condition ψ=0 outside the OPEB as follows:ψ=Csin(kx)  (4)

Here C is a constant. If the width of the OPEB is L, then the boundaryconditions ψ(0)=0 and ψ(L)=0 will give the solution to Schroedinger'sequation in the form of sin(kL)=0, and kL=nπ(n=1, 2, 3,. . . ). Thisgives a well-known discrete series of possible wave vectorscorresponding to possible quantum states:k_(n)=nπ/L  (5)

and according to (3) discrete series of possible energiesE_(n)=n²(h²/8mL²)

A disadvantage of e-beam or ion beam milling is that the distribution ofintensity inside the beam is not uniform, which means that structuresproduced using these methods do not have a uniform shape. In particular,the edges of the milled areas are always rounded, repeating the shape ofintensity distribution inside the beam. Such rounding is more or lessacceptable depending on the type of device fabricated. However, fordevices working on the basis of wave interference this type of roundingis less acceptable, because wave interference depends greatly both onthe dimensions and the shape of the structure.

DISCLOSURE OF INVENTION

In broad terms, the present invention is concerned with methods forincreasing the Fermi level of a metal.

In accordance with one embodiment of the present invention, a wall of apotential energy box is modified, which changes the boundary conditionsfor the wave function of an elementary particle inside the potentialenergy box. New boundary conditions decrease the number of solutions ofSchroedinger's equation.

In accordance with a second embodiment of the present invention, amethod for increasing the Fermi energy in a metal is disclosed. Themethod comprises creating an indented or protruded structure on thesurface of a metal. The depth of the indents or height of protrusions isequal to a, and the thickness of the metal is Lx+a. The minimum valuefor a is chosen to be greater than the surface roughness of the metal.Preferably the value of a is chosen to be equal to or less than Lx/5.The width of the indentations or protrusions is chosen to be at least 2times the value of a.

In accordance with a third embodiment of the present invention, a methodfor making a surface having a geometric pattern that promotes theemission and transmission of electrons across a surface potential energybarrier is provided. The method includes depositing a metal layer on asubstrate. The method also includes exposing specific areas of the metallayer to an electromagnetic energy source and to remove the metal layerin a geometric pattern. The method also includes etching the exposedgeometric pattern to form indents in the surface, using a liquid etchantor plasma. The method also includes removing the remaining metal layerfrom the surface. The method also includes creating De Broglie waveinterference with the geometric pattern in the surface. The method alsoincludes removing the metal layer from the surface.

A technical advantage of the present invention is that the method yieldsa geometric pattern having sharply-defined edges. A further technicaladvantage of the present invention is that it promotes the transfer ofelectrons across a potential barrier, and for a particular energybarrier that exists on the border between a solid body and a vacuum,provides a surface with a sharply defined geometric pattern that causesdestructive interference between reflected electron probability waves(De Broglie waves). Another technical advantage of the present inventionis that it allows for an increase in particle emission through apotential energy barrier. Another technical advantage of the presentinvention is that a surface has a sharply defined geometric pattern of adimension that promotes destructive interference of the reflectedelementary particle probability waves.

A controllable increase in the Fermi level, and the correspondingdecrease of the work function of the metal will have practical use fordevices working on the basis of electron motion, electron emission,electron tunneling etc.

BRIEF DESCRIPTION OF DRAWINGS

For a more complete understanding of the present invention and thetechnical advantages thereof, reference is made to the followingdescription taken with the accompanying drawings, in which:

FIG. 1 is a diagrammatic representation of a three-dimensional potentialenergy box. Potential energy is zero everywhere inside the box volumeand is infinity everywhere outside of box volume.

FIG. 2 is a diagrammatic representation of a three-dimensional potentialenergy box with indented wall. a is the depth of the indent and b iswidth of the indent. Potential energy is zero everywhere inside the boxvolume and is infinity everywhere outside of box volume. Maximumdimension in X direction is L_(x)+a.

FIG. 3 is a diagrammatic representation of a potential energy boxtogether with solutions of Schroedinger equation. Boundary conditionsψ(L_(x))=0 and ψ(L_(x)+a)=0 define solutions of Schroedinger equationsas shown on the right side of the figure.

FIG. 4 is a diagrammatic representation of a possible realization ofmetal with indented wall. Indents are etched on the surface of thinmetal film deposited on insulating substrate.

FIG. 5 is an Energy diagrams of some single valence metals on the scaleof de Broglie wavelength calculated as λ=2π/k from (3).

FIG. 6 is a diagrammatic representation of a possible realization ofmetal with indented wall. Indents are etched on the surface of aninsulating substrate, on which is deposited a thin metal film.

FIG. 7 depicts a surface and a layer in accordance with an embodiment ofthe present invention.

FIG. 8 depicts an exposure of a layer to an energy source in accordancewith an embodiment of the present invention.

FIG. 9 depicts a geometric pattern and a layer on a surface inaccordance with an embodiment of the present invention.

FIG. 10 depicts etching a surface in accordance with an embodiment ofthe present invention.

FIG. 11 depicts an etched geometric pattern in a surface in accordancewith an embodiment of the present invention.

FIG. 12 depicts a wave interference barrier in a surface in accordancewith an embodiment of the present invention.

FIG. 13 depicts a process for making paired electrodes.

FIG. 14 depicts a process for making paired electrodes.

FIG. 15 depicts a process for making a diode device.

BEST MODE OF CARRYING OUT THE INVENTION

The embodiments of the present invention and its technical advantagesare best understood by referring to FIGS. 2-14.

Referring now to FIG. 2, which shows a modified potential energy box(MPEB) 10, five walls of the potential energy box are plane and thesixth wall 12 is indented. The indents on the sixth wall 12 have theshape of strips having depth of a and width of b. The length of the boxin the X direction Lx+a, in the Y direction is Ly and in the Z directionis Lz. The potential energy of a particle inside the box volume is equalto zero, and outside the box volume is equal to U. There is a potentialenergy jump from zero to U at any point on the walls of the box.

Referring now to FIG. 3, which shows the further boundary conditionsthat are introduced as a result of the modification of wall 12, the wavefunction should now be equal to zero not only at x=0 and x=L_(x)+a, butalso at the point x=L_(x). Yet another additional boundary condition isadded because the modified wall could be divided into two parts withequal area. The first part is situated at distance L_(x) from theopposite wall, while the second part is situated at distance L_(x)+afrom the opposite wall. Once U=∞ is true for every point of both partsof the modified wall, ψ=0 is true also for every point of both parts ofthe modified wall. This means that ψ(L_(x))=0 and ψ(L_(x)+a)=0. Inaddition, there is the boundary condition for the unmodified wall,ψ(0)=0. Thus three boundary conditions in the X direction:ψ(0)=0, ψ(L_(x))=0 and ψ(L_(x)+a)=0 (6)

There is no general solution of (1) which will be true for any pair ofL_(x) and a, unlike the case of OPEB in which has solutions for any L.However, it is obvious that the last two boundary conditions of equation(6) define possible solutions, just as they do for the OPEB of width ofL=a. The wave function should be zero at points L_(x) and L_(x)+a, andpossible solutions are sinusoids 30 having a discrete number of halfperiods equal to a, as shown in FIG. 3. The first boundary conditionfrom (6) will be automatically satisfied together with the last twoboundary conditions only in the case that:L_(x)=pa   (7)

where p=1, 2, 3,. . . There will be some solutions also for the caseL_(x)≠pa. For example in the case L_(x)=pa/2 there are solutionssatisfying all three boundary conditions for n=2, 4, 6, . . . It isobvious that number of solutions satisfying all boundary conditions (6)will be maximum in the case Lx=pa, and so in the following it is assumedthat L_(x)=pa, which maximizes the possible solutions.

Assuming then that MPEB has dimensions satisfying condition (7),solutions will be:k_(n)=nπ/a   (8)

just as for the OPEB (5) of width L=a. However, the whole width of thebox is replaced by a part of it (L_(x)+a is replaced by a). It isinteresting to compare solutions for MPEB (8) and OPEB of width ofL=L_(x)+a (in this one dimensional case). Solutions for OPEB havingwidth of L=L_(x)+a will be:k_(n)=nπ/ (L_(x)+a)  (9)

and the solution for the MPEB will be (8). There are thus fewer possiblevalues for k in the case of the MPEB compared to an OPEB of the samewidth. Thus modifying the wall of the potential energy box as shown inFIG. 2 leads to a decrease in the number of possible quantum states.More precisely, altering the potential energy box leads to a decrease inthe number of possible wave vectors per unit length on k line(L_(x)+a)/a times. This last equation is easily obtained from (8) and(9).

Applying a three-dimensional analysis, if a<<L_(x), L_(y), L_(z), itwill not influence the solutions of Schroedinger equation for both Y andZ dimensions appreciably, and k_(x)=n(π/a), ky=n(π/L_(y)),k_(z)=n(π/L_(z)), and the volume of elementary cell in k space will be:V_(m)=π³/(a L_(y) L_(z))  (10)

which is again (L_(x)+a)/a times more than the volume of the elementarycell in k space for the OPEB, where V_(m)=π³/[(L_(x)+a) L_(y) L_(z))].Volume in k space for three-dimensional case changes like lineardimension on k line in the one-dimensional case. Because of that resultscan be easily extrapolate from the one-dimensional case to thethree-dimensional case.

The importance of this is illustrated by the following thoughtexperiment in which there are two potential energy boxes of the samedimensions, one an OPEB with all walls plane, and another a MPEB withone wall modified. An equal number of fermions are placed, one at atime, in both of the potential energy boxes and the wave vector andenergy of the most recently added fermion in both boxes is observed. Thefirst fermion in both boxes will occupy quantum state k₀=0 in ordinarybox and k_(m0)=0 in MPEB. The second fermion in OPEB will occupyk₁=π/(L_(x)+a) and in MPEB k_(m1)=π/a. If equal number of fermions arecontinued to be added to both boxes, then k_(n)=nπ/(L_(x),+a) for theOPEB and k_(mn)=nπ/a for the MPEB. It is obvious that the n^(th) fermionwill have (L_(x)+a)/a times more wave vector in the MPEB than in theOPEB. Correspondingly, the energy of the n^(th) fermion in the MPEB willbe [(L_(x)+a)/a ]² times higher than in the OPEB. This is only true forthe one-dimensional case. For the three-dimensional case, the ratio ofenergies of the n^(th) pair of fermions will be:(E _(m) /E)=[(L _(x) +a)/a] ^(2/3)   (11)

here E_(m) is the energy of n^(th) fermion in the MPEB and E is theenergy of the n^(th) fermion in the OPEB. Index n is skipped in formula(11) because the ratio of energies does not depend on it.

Free electrons inside the solid state is one of the examples of fermionsinside the potential energy box. For metals, the theory of electron gasinside the lattice is well developed and is based on different models,the most simple of which is the quantum model of free electrons, whichgives excellent results when applied to most metals. It is well knownthat free electrons in metal form a Fermi gas. Boundary condition ψ=0outside the metal is used in all theories because in metals thepotential energy barrier is high enough to allow that simpleapproximation. In the quantum theory of free electrons, cyclic boundaryconditions of Born-Carman:k _(x)=2πn/L  (12)

are used instead of (5). Here n=0, ±1, ±2, ±3, . . . Cyclic boundaryconditions leave the density of quantum states unchanged, and at thesame time they allow the study running waves instead of standing waves,which is useful for physical interpretation. The result of the theory isFermi sphere in k space. All quantum states are occupied until k_(F) atT=0 K. k_(F) is maximum wave vector inside the metal at T=0 K becausestates with k>k_(F) are empty.

For a MPEB, the distance between quantum states in k space in k_(x)direction will become 2π/a instead of 2π/ (L_(x)+a). The number ofquantum states per unit volume in k space will decrease (L_(x)+a)/atimes. Metal retains its electrical neutrality, which means that thesame number of free electrons have to occupy separate quantum statesinside the metal. Because the number of quantum states per unit volumein k space is less than in the case of ordinary metal, some electronswill have to occupy quantum states with k>k_(F). This shows that theFermi wave vector and the corresponding Fermi energy level willincrease.

The maximum wave vector k_(m) at T=0 K for metal with a modified wallcan be calculated. Posit that the lattice is cubic, the metal is singlevalence, and the distance between atoms is d. The volume of metal boxshown in FIG. 2 is:V=L_(y)L_(z)(L_(x)+a/2)  (13)

Number of atoms inside the metal is q=V/d³. The number of free electronsis equal to q which gives:q=L_(y)L_(z)(L_(x)+a/2)/d³   (14)

for the number of free electrons. The volume of elementary cell in kspace is:Ve=(2π/a)(2π/L_(y))(2π/L_(z))  (15)

And the volume of the sphere of the radius of k_(m) in k space is:V_(m)=(4/3)πk_(m) ³   (16)

here k_(m) is maximum possible k in the case of modified wall and V_(m)is the volume of modified Fermi sphere in k space. Number of possiblek=k_(x)+k_(y)+k_(z) in k space is V_(m)/V_(e). Each k contains twoquantum states occupied by two electrons with spins ½ and −½. Using(14), (15), (16) gives:(q/2)=(k_(m) ³aL_(x)L_(z)/6π²)  (17)

and for the radius of modified Fermi sphere:k_(m)=(1/d)[3π²(L_(x)/a+½)]^(1/3)   (18)

It is well known that the radius of a Fermi sphere k_(F) for an ordinarymetal does not depends on its dimensions and is k_(F)=(1/d) (3π²)^(1/3).Comparing the last with (18) gives:k_(m)=k_(F)(L_(x)/a+½)^(1/3)   (19)

Formula (19) shows the increase of the radius of the Fermi sphere in thecase of metal with modified wall in comparison with the same metal withplane wall. If it is assumed that a<<L_(x), L_(y), L_(z) formula (19)could be rewritten in the following simple form:k_(m)=k_(F)(L_(x)/a)^(1/3)   (20)

According to (3) the Fermi energy in the metal with the modified wallwill relate to the Fermi energy in the same metal with the plane wall asfollows:E_(m)=E_(F)(L_(x)/a)^(2/3)   (21)

Thus it is shown that modifying the geometry of the metal wall resultsin an increase of the Fermi level in the metal.

It is interesting to consider what would happen if the ratio L_(x)/a ismade high enough for E_(m) to exceed vacuum level. Assuming that someelectrons have energies greater than the vacuum level, they will leavemetal. The metal, as a result, will charge positively, and the bottom ofthe potential energy box will go down on the energy scale, because metalis charged now and it attracts electrons. Once the bottom of thepotential energy box decreases, vacant places for electrons will appearat the top region of potential energy box. Electrons left the metal willreturn back because of electrostatic force and occupy the free energystates. Accordingly, E_(m) will not exceed the vacuum level. Instead,the bottom of the potential energy box will go down exactly at suchdistance to allow the potential energy box to carry all electrons neededfor electrical neutrality of the metal. Regarding the work function itis clear that increasing the ratio of L_(x)/a will decrease first untilit gets equal to zero. Even with a further increase in L_(x)/a, the workfunction will remain zero. In real metals surfaces are never ideallyplane. Roughness of the surface limits the increase of Fermi level.

It is useful to recall here that analysis was made within the limits ofquantum theory of free electrons. Model of free electrons give excellentresults for single valence metals. More developed theories, which takeinto account electron-lattice and electron-electron interaction could beused to obtain more precise results. However results given here willremain valid within all theories at least for the region (−π/d)<k<(π/d),where d is lattice constant. Dimensional effects in semiconductor andsemimetals were studied theoretically [V. A. Volkov and T. N. Pisker“Quantum effect of dimensions in the films of decreasing thickness”Solid State Physics (Russian), 13, p.1360 (1971); V. N. Lutskii. JETPLetters (USSR) 2, p. 245 (1965)]. Particularly influence of thin filmdimensions on its Fermi level, is studied in [V. N. Lutskii. JETPLetters (USSR) 2, p. 245 (1965)].

Referring now to FIG. 4, which shows a structure that satisfies therequirements given above, a thin metal film 40 is deposited on theinsulator substrate 42, and indents 44 are etched into the film. Indentshave depth a and width b.

Most metals oxidize under the influence of atmosphere. Even when placedin vacuum metals oxidize with time because of influence of residualgases. Typical oxides have depth of 50-100 Å, which is considerable onthe scale discussed. In one embodiment, film 40 comprises anoxidation-resistant metal. In a preferred embodiment, film 40 comprisesgold.

In one embodiment, film 40 is deposited so that it is homogenous and notgranular: if the metallic film is granular, the wave function will havean interruption on the border of two grains, and the indented wall'sinfluence on the boundary conditions will be compromised because thewave function will not be continuous on the whole length of L_(x)+a. Ina preferred embodiment, film 40 is a monocrystal. It is necessary tonote here that lattice impurities do not influence free electrons withenergies E<E_(F). In order to interact with an impurity inside thelattice, the electron should exchange the energy with the impurity inthe lattice. That type of energy exchange is forbidden because allquantum states nearby are already occupied. The mean free path of anelectron, sitting deep in Fermi sea is formally infinite. So thematerial of the film can have impurities, but it should not be granular.That type of requirement is quite easy to satisfy for thin metal films.

In a preferred embodiment, film 40 is plane. The surface of the filmshould be as plane as possible, as surface roughness leads to thescattering of de Broglie waves. Scattering is considerable for thewavelengths of the order or less than the roughness of the surface.Substrates with a roughness of 5 Å are commercially available. Metalfilm deposited on such substrate can also have a surface with the sameroughness. The de Broglie wavelength of a free electron in metal sittingon the Fermi level is approximately 10 Å. Scattering of the de Brogliewave of electrons having energies E>E_(F) will be considerable.Consequently, energy states with energies E>E_(F) will be smoothed.Smoothing of energy levels decrease the lifetime of the energy state andlead to continuous energy spectrum instead of discrete one. FIG. 5 showsa comparison of Fermi and vacuum levels of some single valence metals onthe energy scale and simultaneously on the scale of de Brogliewavelength of the electron calculated from formula (3). It is evidentthat 5 Å roughness of the surface is enough to eliminate energy barrier(in the case L_(x)≠pa) for such metals as Cs and Na. The same roughnesscreates gap from zero to approximately Fermi level in energy spectrum ofsuch metals as Au and Ag.

Values for a and b are chosen to reduce diffraction of the standing wave(see formulas (2) and (4) that show that plane waves are solutions ofthe Schroedinger equation). A standing wave comprises two plane wavesmoving in the direction of X and −X. Wave diffraction will take place onthe indent. Diffraction on the indents will lead to the wave “ignoring”the indent, which changes all calculations above. In a preferredembodiment values for a and b are chosen so that the diffraction of thewave on the indent is negligible, or:b>>λ₁   (22)

Here λ₁=2π/k₁ is de Broglie wavelength of electron with wave vector k₁(n=1 in FIG. 3). It is obvious that (22) will be automatically valid forn=1, 2, 3, . . .

The thickness of film 40 is chosen so that equation (7) is valid. In oneembodiment, L_(x) is a multiple of a. If equation (7) is not valid, thenthe number of quantum states will be less than the number given byformula (8). Decreasing the number of quantum states will magnify theeffect of increasing of EF, but it will be problematic to control workfunction decrease without keeping (7) valid during the metal filmdeposition stage, as well as during indent etching. In addition, if (7)is deliberately kept not valid it will lead to the elimination ofpossible quantum states from E=0 to energy level defined by roughness ofthe surface. In a further embodiment L_(x) is chosen so that it is not amultiple of a.

In a preferred embodiment depth of the indent should be much more thanthe surface roughness. Consequently, the minimum possible a is 30-50 Å.Preferably the indents have a depth of a depth approximately 5 to 20times the surface roughness. According to (22) the minimum possible bwill be 300-500 Å. Preferably the width is approximately 5 to 15 timesthe depth. These dimensions are well within the capabilities of e-beamlithography and ion beam milling. The primary experimental limitation inthe case of the structure shown on FIG. 4 is that the ratio (L_(x)/a)≧5,in order to achieve a work function which is close to zero.Consequently, the thickness of the metal film should be at least 180-300Å, and is preferably 150 to 750 Å. Usually films of such thickness stillrepeat the substrate surface shape, and the film surface roughness doesnot exceed the roughness of the base substrate. However, the same is nottrue for metal films with a thickness of 1000 Å and more, because athick film surface does not follow the surface of the substrate. Thatputs another limit 15≧(L_(x)/a)≧25 on the dimensions of the structure,when metal films are deposited on the substrates. Other possiblesolutions, such as metal crystals of macroscopic dimensions like thosefrequently used for electron beam microscope cathodes, will not belimited by the same requirements.

Referring now to FIG. 6, which shows a further embodiment of a structurethat satisfies the requirements given above, a thin metal film 60 isdeposited on a structured insulator substrate 62. The structuredsubstrate as indentations of depth a and the distance between theindents is b. This means that the metal film has thickness L_(x) and hasindents of depth a and width b, but now the active surface is plane.

A particularly preferred approach for fabricating a structure thatsatisfies the requirements given above is shown in diagrammatic form inFIG. 7, which depicts a surface 102 of a material 103 and a metal layer104 in accordance with one embodiment of the present invention. Material103 may be comprised of a variety of substances, and may be metallic ora semiconductor. In one embodiment material 103 is resistant to etchingin any direction except the direction perpendicular to the surface 102.In a further embodiment, surface 102 is able to emit electrons viathermionic, secondary, photoelectric and/or field emission. In a yetfurther embodiment, surface 102 is comprised of silicon. Layer 104comprises a material that is different to material 103, and isrelatively more sensitive to e-beam or ion beam or more readily ablatedthan material 103. Preferably, layer 104 does not promote a chemicalreaction with surface but is adsorbed to the surface. In a preferredembodiment, layer 104 comprises soft metals such as lead, tin or gold.Layer 104 is deposited on surface 102 such that layer 104 is in adhesivecontact with surface 102. Layer 104 covers surface 102 in a uniformmanner such that surface 102 is protected from the environment.Preferably layer 104 is a thin film having a depth of 20 to 200Angstroms. Preferably surface 102 is substantially flat, but layer 104may be also deposited after milling on surface 102.

Referring now to FIG. 8, which depicts exposure of selected areas oflayer 104 to an e-beam source 302, e-beam 304 operates at a lowintensity and cuts the ablatable material of layer 104. Ion beam or beamof other particles could be used instead of e-beam. Preferably, thesource positions the beam at the center of a hole 308 within layer 104.Hole 308 represents that part of layer 104 that has been removed by thebeam. Because no beam is focused ideally layer 104 is being removed morein the center and less on the periphery of the beam.

Because material 103 is much harder than material 104, the central areaof 308 is minimally damaged by the beam in the time period startingafter finishing milling of 104 in the center of 308 and before finishingthe milling of 104 on the periphery of 308.

Referring now to FIG. 9, which depicts a geometric shape in layer 104 onsurface 102 in accordance with an embodiment of the present invention,the beam repeats the process of cutting holes into layer 104 shown inFIG. 2, to create the geometric shape in the material 103 as shown. Thegeometric shape includes strips 402, which are the remaining material oflayer 104. These preferably comprise lead, tin, or gold. Mostpreferably, strips 402 comprise gold. Geometric shape 420 has edgesenclosed by strips 402. Alternatively, the beam can produce othergeometric shapes in the layer 104, such as squares, rectangles, a singlestrip, or a stepped shape.

Referring now to FIG. 10, which depicts the etching surface 102 inaccordance with an embodiment of the present invention, etchant 510reacts with surface 102, but not with strips 402 nor with the portion ofthe surface 102 that is covered with strips 402. The etchant etchessurface 102 in a precise and uniform manner. The etchant may be achemical that reacts with surface 102, or it may be a plasma.Preferably, etchant 510 is a liquid.

Referring now to FIG. 11, which depicts an etched geometric pattern inaccordance with an embodiment of the present invention, indents 606 arecreated by the reaction of etchant 510 with surface 102 as describedabove to yield surface 602 having the geometric pattern etched into itssurface. The depths a of indents 606 are controlled by the applicationof etchant 510. Strips 402 reside on top of the non-indented regionswithin geometric pattern surface 602. The indents created by etchant 510correlate with geometric shapes 420 cut by beam 304 as described above.

Referring now to FIG. 12, which depicts a wave interference surface inaccordance with an embodiment of the present invention, strips 402 areremoved from geometric pattern surface 602 to expose non-indentedregions 710. Strips 402 may be removed by vacuum evaporation or otherremoval techniques that do not damage the underlying surface.Protrusions 710 are the raised surfaces of geometric pattern surface602. Thus, geometric pattern surface 602 has a distinct geometricpattern formed by indents 606 and protrusions7lo. Geometric patternsurface 602 includes spaced indents 606 and protrusions 710. The depthof the indents and the width of the protrusions are about equal acrossgeometric pattern surface 602. The magnitude of defined depth a ofindent 606 and it's associated width b are discussed above.

A further approach, useful for making the device shown in FIG. 6, isshown diagrammatically in FIG. 13. Here, in step 1300, a layer oftitanium 1304 is deposited on a wafer 1302. The wafer may comprisesilicon or molybdenum. Next, in step 1310, a layer of silver 1312 isdeposited on the layer of titanium. The next step, step 1320, involvesthe formation of an indented surface in the silver layer, which may beachieved as described above, particularly as shown in FIGS. 7 to 12. Instep 1330 a layer of copper 1332 is grown electrochemically on the layerof silver to form composite 1334, which is an electrode pair precursor.In step 1340, composite 1334 is heated, which causes it to open asshown, forming a pair of matching electrodes, 1342 and 1344.

An alternative approach for forming matched electrodes, one of which hasthe properties associated with an indented structure, is shown in FIG.14. Here in step 1400 an indented surface is formed on the wafer 1402.The indented surface may be formed as described above, particularly asshown in FIGS. 7 to 12. Next, in step 1410, a layer of silver isdeposited on the indented wafer 1402, and in a further step 1420, alayer of titanium 1422 is deposited on the silver layer. In step 1430 alayer of copper 1432 is grown electrochemically on the layer of silverto form composite 1434, which is an electrode pair precursor. In step1440, composite 1434 formed is heated, which causes it to open as shown,forming a pair of matching electrodes, 1442 and 1444.

The electrode pairs made in steps 1340 and 1440 may be utilized to makediode devices, and a preferred process is depicted in FIG. 15, where instep 1500 a first substrate 1502 is brought into contact with a polishedend of a quartz tube 90. Substrate 1502 is any material which may bebonded to quartz, and which has a similar thermal expansion coefficientto quartz. Preferably substrate 1502 is molybdenum, or silicon doped torender at least a portion of it electrically conductive. Substrate 1502has a depression 1504 across part of its surface. Substrate 1502 alsohas a locating hole 1506 in its surface.

In step 1510, liquid metal 1512, is introduced into depression 1502. Theliquid metal is a metal having a high temperature of vaporization, andwhich is liquid under the conditions of operation of the device. Thehigh temperature of vaporization ensures that the vapor from the liquiddoes not degrade the vacuum within the finished device. Preferably theliquid metal is a mixture of Indium and Gallium. Composite 78 ispositioned so that alignment pin 1514 is positioned above locating hole1506. Composite 78 is composite 1334 depicted in FIG. 13, or iscomposite 1434 depicted in FIG. 14; for simplicity, the indentedinterface is not shown. Alignment pin 1514, which is pre-machined, isplaced on the composite near the end of the electrolytic growth phase;this results in its attachment to the layer of copper 1332 or 1432. Thediameter of the alignment pin is the same as the diameter of thelocating hole.

In step 1520, the polished silicon periphery of the composite 78 iscontacted with the other polished end of the quartz tube 90; at the sametime, the attachment pin seats in locating hole. During this step,substrate 1502 is heated so that locating hole expands; when theassemblage is subsequently cooled, there is a tight fit between thealignment pin and the locating hole. High pressure is applied to thisassemblage, which accelerates the chemical reaction between the polishedsilicon periphery of the composites and the polished ends of the quartztube, bonding the polished surfaces to form the assemblage depicted instep 1520.

In step 1530, the assemblage is heated, and a signal applied to thequartz tube to cause the composite to open as shown, forming twoelectrodes, 72 and 74. In the deposition process, the adhesion of thesilver and titanium is controlled so that when the electrodecomposite/quartz tube shown in FIG. 15 is heated, the electrodecomposite opens as shown, forming a pair of matching electrodes, 72 and74. During the opening process, the tight fit between the alignment pinand the locating hole ensures that the electrodes 72 and 74 do not sliderelative to one another.

The quartz tube has pairs of electrodes disposed on its inner and outersurfaces (not shown) for controlling the dimensions of the tubularelement. The crystal orientation of the tube is preferably substantiallyconstant, and may be aligned either parallel to, or perpendicular to theaxis of the tube. An electric field may be applied to the tube, whichcauses it to expand or contract longitudinally. An advantage of such atubular actuator is that it serves both as actuator and as housingsimultaneously. Housing provides mechanical strength together withvacuum sealing. External mechanical shock/vibrations heat the externalhousing first, and are compensated immediately by actuator.

It has been shown that modifying the wall of a potential energy boxchanges the boundary conditions for the wave function of an elementaryparticle inside the potential energy box. New boundary conditionsdecrease the number of solutions to Schroedinger's equation for aparticle inside the MPEB. If the particles are fermions, the decrease inthe number of quantum states results in an increase in the energy of then^(th) particle situated in the potential energy box. General resultsobtained for fermions in the potential energy box were extrapolated tothe particular case of free electrons inside the metal. Calculationswere made within the limit of quantum theory of free electrons. It wasshown that in the case of a certain geometry of the metal wall, theFermi level inside the metal will increase. A controllable increase inthe Fermi level, and the corresponding decrease of the work function ofthe metal will have practical use for devices working on the basis ofelectron motion, electron emission, electron tunneling etc.

Although the above specification contains many specificities, theseshould not be construed as limiting the scope of the invention but asmerely providing illustrations of some of the presently preferredembodiments of this invention.

Indentations and protrusions to a basic surface are both described inthe specification, and there is really little technical differencebetween the two, except in their production method. Where an indentedsurface is referred to, it should be read as also referring to a surfacehaving protrusions, which, by definition, causes the surface to have anindented cross-section, having indents in the ‘spaces’ between theprotrusions.

INDUSTRIAL APPLICABILITY

The method for enhancing passage of elementary particles through apotential barrier has many applications; for example, the method may beapplied to thermionic converters, vacuum diode heat pumps andphotoelectric converters, where a reduction in work function gives realbenefits in terms of efficiency or operating characteristics.

The elementary particle emitting surface has many further applications.The surface is useful on emitter electrodes and other cathodes becauseit promotes the emission of electrons. It is also useful on collectorelectrodes and other anodes because it promotes the passage of electronsinto the electrode. The surface also has utility in the field of coldcathodes generally, and electrodes incorporating such a surface can beused.

In the foregoing indents of a required depth and pitch have beendescribed which run across the surface of the slab in a trench-likefashion. Other geometries having indents of the required depth and pitchalso fall within the intended scope of the invention. For example,instead of long trenches, these could be checkerboard shape, with theblack squares for example, representing surface indentations, and whitesquares, protrusions. There could be hexagons, octagons or heptagons, oreven circles, imprinted into or protruding out of the surface.

1. An electrode pair precursor comprising: (a) a silicon wafer; (b) afirst layer of a substantially plane slab in contact with said siliconwafer; (c) a second layer in contact with said first layer; (d) a thirdlayer in contact with said second layer; wherein one surface of saidsilicon wafer or one surface of said second layer has one or moreindents of a depth approximately 5 to 20 times a roughness of saidsurface and a width approximately 5 to 15 times said depth.
 2. Theelectrode pair precursor of claim 1 wherein said first layer comprisestitanium.
 3. The electrode pair precursor of claim 1 wherein said secondlayer comprises silver.
 4. The electrode pair precursor of claim 1wherein said third layer comprises copper.
 5. The electrode pairprecursor of claim 1 wherein the method for forming said third layer ofcopper comprises electrolytic growth of copper.
 6. The electrode pairprecursor of claim 1 wherein said depth ≧λ/2, wherein 1 is the deBroglie wavelength.
 7. The electrode pair precursor of claim 1 whereinsaid depth is greater than the surface roughness of the metal surface.8. The electrode pair precursor of claim 1 wherein said width >>λ,wherein λ is the de Broglie wavelength.
 9. The electrode pair precursorof claim 1 wherein a thickness of said slab is a multiple of said depth.10. The electrode pair precursor of claim 1 wherein a thickness of saidslab is not a multiple of said depth.
 11. The electrode pair precursorof claim 1 wherein a thickness of said slab is between 5 and 15 timessaid depth.
 12. The electrode pair precursor of claim 1 wherein athickness of said slab is in the range 15 to 75 nm.
 13. A method offabricating the electrode pair precursor of claim 1 comprising thesteps: (a) providing a silicon wafer; (b) depositing a first layerforming a substantially plane slab on said silicon wafer; (c) depositinga second layer on said first layer; (d) forming a third layer on saidsecond layer. (e) creating on either or both of one surface of saidwafer and one surface of said second layer one or more indents of adepth approximately 5 to 20 times a roughness of said surface and awidth approximately 5 to 15 times said depth;
 14. The method of claim 13wherein said first layer comprises titanium.
 15. The method of claim 13wherein said second layer comprises silver.
 16. The method of claim 13wherein said third layer comprises copper.
 17. The method of claim 13wherein the method for forming said third layer of copper compriseselectrolytic growth of copper.
 18. The method of claim 13 wherein saidstep of creating one or more indents is done by etching to a depth ≧λ/2,wherein λ is the de Broglie wavelength.
 19. The method of claim 13wherein said step of creating one or more indents is done by etching toa depth that is a multiple of said thickness.
 20. The method of claim 13wherein said step of creating one or more indents is done by etching toa depth that is not a multiple of said thickness.
 21. The method ofclaim 13 wherein said step of creating one or more indents is done byetching to a depth that is between a fifth and a fifteenth of saidthickness.
 22. The method of claim 13 wherein said step of creating oneor more indents is done by etching to a depth that is in the range 135to 75 nm.
 23. The method of claim 13 wherein said step of etching at asubstantially 90 degree angle to said surface said exposed portions to auniform depth is done by reacting a chemical etchant with the exposedsurface.
 24. The method of claim 13 wherein said step of etching at asubstantially 90 degree angle to said surface said exposed portions to auniform depth is done by reacting a plasma etchant with the exposedsurface.